Find two positive numbers whose sum is 676 and the

Chaya Galloway 2021-08-14 Answered
Find two positive numbers whose sum is 676 and the sum of whose squares is a minimum.

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Expert Answer

SoosteethicU
Answered 2021-08-15 Author has 8471 answers
Let the two numbers be x and y. Sum is 676 x+y=676 Solve for y y=676-x Now, sum of squares \[=x^{2}+y^{2}\\ =x^{2}+(676-x)^{2}\\ =x^{2}+456976+x^{2}-1352x\\ 2x^{2}-1352x+456976 \\ \text{where}\ a=2x^{2},b=1352x,c=456976\] Minimum occurs at vertex \[\text{So,}\ x=\frac{-b}{2a}\\ x=\frac{1352}{2(2)} \\ x=\frac{1352}{4} \\ x=338 \\ y=676-x\\ y=676-338\\ y=338\] So, (338, 338) is Answer
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